Monte Vista April 3, rd Grade 4 th Grade 5 th Grade Liz Morris Math Coach Lisa Liberta Assistand Principal

 What are Arizona College and Career Ready Standards (ACCRS) and why are they different?  Do the math!  Procedural Math vs. Conceptual Math  How can I support my child in math?  Questions?

 The AZCCRS Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them.  The standards are designed to be focused, coherent, and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers.  With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.

 research and evidence based,  aligned with college and work expectations,  rigorous, and  Internationally benchmarked.

5.NBT.B.5 B: Perform operations with multi-digit whole numbers and with decimals to hundredths. Fluently multiply multi-digit whole numbers using the standard algorithm. In prior grades, students used various strategies to multiply. Students can continue to use these different strategies as long as they are efficient, but must also understand and be able to use the standard algorithm. In applying the standard algorithm, students recognize the importance of place value. Example: 123 x 34. When students apply the standard algorithm, they, decompose 34 into Then they multiply 123 by 4, the value of the number in the ones place, and then multiply 123 by 30, the value of the 3 in the tens place, and add the two products. 45 X 36 = _____360 X 18 = ____

 “Action sequences for solving problems.”  Rittle-Johnson & Wagner (1999)  “Like a toolbox, it includes facts, skills, procedures, algorithms or methods.”  Barr, Doyle et. el. (2003)  “Learning that involves only memorizing operations with no understanding of underlying meanings.”  Arslan (2010)  “Ideas, relationships, connections, or having a ‘sense’ of something.”  Barr, Doyle et. el. (2003)  “Learning that involves understanding and interpreting concepts and the relations between concepts.”  Arslan (2010)  “To know why something happens in a particular way.”  Hiebert and Lefevre (1986)

CONCEPTUAL Equations:  45 X 36 =  45 X 36 Equations:  45 X 36 = Strategies: Break apart both numbers by place value (40 + 5) X (30 + 6) PROCEDURAL X 30 = 1, X 6 = X 5 = X 5 = 30 1, = 1,440 1, = 1,590 1, = 1,620

PROCEDURALCONCEPTUAL Equations:  360 X 18 =  360 X 18 Equations:  360 X 18 = Strategies: Halving and Doubling  Double 360 to 720  Half 18 into X 9 = 700 X 9 = X 9 = = 6,480

 Algorithm - a step-by-step procedure for solving a problem  US Standard Algorithms Carrying the 1 in addition – 4 th Grade Borrowing in subtraction – 4 th Grade Carrying in multiplication – 5 th Grade Long division – 6 th Grade  Strategies – build to an understanding of the operations used in solving problems

 Direct Modeling - 6 x 3  Pictures, Number Line

 Distributive Property (Break Apart) - 6 x 7

National Research Council ( Unknown ProductGroup Size Unknown (“How many in each group?” Division) Number of Groups Unknown (“How many groups?” Division) 3 x 6 = ?3 x ? = 18, and 18 ÷ 3 = ?? x 6 = 18, and 18 ÷ 6 = ? Equal Groups There are 3 bags with 6 plums in each bag. How many plums are there in all? Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether? If 18 plums are shared equally into 3 bags, then how many plums will be in each bag? Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be? If 18 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have? Arrays, 4 Area 5 There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example. What is the area of a 3 cm by 6 cm rectangle? If 18 apples are arranged into 3 equal rows, how many apples will be in each row? Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it? If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it? Compare A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost? Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long? A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does a blue hat cost? Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first? A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first? General General a x  b = ?a x  ? = p, and p ÷  a = ?? x  b = p, and p ÷  b = ?

Type I: Tasks assessing concepts, skills and procedures

The art teacher will tile a section of the wall with painted tiles made by students in three art classes.  Class A made 18 tiles  Class B made 14 tiles  Class C made 16 tiles Part A What is the total amount of tiles that are being used? Part B The grid shows how much wall space the art teacher can use. Use the grid to create a rectangular array showing how the art teacher might arrange the tiles on the wall. Select the boxes to shade them. Each tile should be shown by one shaded box. Part C Andy created a rectangular array showing how he would place 56 small tiles on the wall. He placed 7 tiles in each row. He wrote a multiplication equation using R standing for the number of rows he used. Write an equation R that Andy could have written.

Type III: Tasks assessing modeling Type III: Tasks assessing modeling / applications / applications

Ask questions when your child gets stuck.  How would you describe the problem in your own words?  What do you know from the problem?  What do you want to find out?  Would it help to create a diagram? Draw a picture? Make a table?  What did classmates try when solving these problems?

So they have an answer to the problem. Great! Check for understanding by asking questions!  How did you get your answer?  Does your answer seem reasonable?  Does that make sense?  Why is that true?  How would you prove that?  Can you think of another strategy that might have worked?  Is there a more efficient strategy?  Do you think this may work with other numbers?  Do you see a pattern? Can you explain the pattern?

 Dreambox can be accessed at home

 Third grade: Know from memory all products of two one-digit numbers. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.  Fourth grade: fluently add and subtract multi- digit whole numbers using the standard algorithm  Fifth grade: fluently multiply multi-digit whole numbers using the standard algorithm

 Cards  Cribbage  Using a Football or Soccer ball  Dice  License plate game “Playing games have proven to me that it really does build fluency.” ~Mrs. Tullo (Kinder)  Board games (i.e. Candy Land, Trouble, Chutes and Ladders, Monopoly, Yahtzee)  Bingo

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Liz Morris Math Coach Lisa Liberta Assistant Principal